The wheel of the engine of a train $4 \frac{2}{7} m$ in circumference makes 7 revolutions in 3 seconds. Find the speed of the train in km per hour.
View full solution →Question types
Circumference and Area of a Circle question types
129 questions across 5 question groups — pick any mix to generate a MATHEMATICS paper with step-by-step answer keys.
129
Questions
5
Question groups
5
Question types
Sample Questions
Circumference and Area of a Circle questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The diameter of a wheel is 1.26 m. How far will it travel in 500 revolutions ?
AC and BD are two perpendicular diameters of a circle ABCD. Given that the area of the shaded portion is $308 cm ^2$calculate:
(i) the length of AC; and
(ii) the circumference of the circle.
View full solution →(i) the length of AC; and
(ii) the circumference of the circle.
The area enclosed between two concentric circles is $770 cm ^2$If the radius of the outer circle is 21 cm, calculate the radius of the inner circle.
View full solution →A wheel makes 1000 revolutions in covering a distance of 88 km. Find the radius of the wheel.
The circumference of a circle exceeds its diameter by 180 cm. Calculate
(i) the radius
(ii) the circumference and
(iii) the area of the circle.
(i) the radius
(ii) the circumference and
(iii) the area of the circle.
Find the perimeter and area of a semi-circular plate of radius 25 cm (Take $\pi$ = 3.14 ).
View full solution →Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of $9856 m ^2$.
View full solution →A wheel makes 1000 revolutions in covering a distance of 88 km. Find the radius of the wheel.
A toothed wheel of diameter 50 cm is attached to a smaller wheel of diameter 30 cm. How many revolutions will the smaller wheel make when the larger one makes 30 revolutions?
The perimeter of a semi-circular metallic plate is 86.4 cm. Calculate the radius and area of the plate.
The area of a circle is$394.24 cm ^2$.
Calculate :
(i) the radius of the circle,
(ii) the circumference of the circle.
View full solution →Calculate :
(i) the radius of the circle,
(ii) the circumference of the circle.
In the given figure, ABCD is a rectangle inscribed in a circle. If two adjacent sides of the rectangle be 8 cm and 6 cm, calculate:
(i) the radius of the circle; and
(ii) the area of the shaded region. (Take $\pi$ = 3.14 )
View full solution →(i) the radius of the circle; and
(ii) the area of the shaded region. (Take $\pi$ = 3.14 )
In the given figure, ABCD is a square of side 5 cm inscribed in a circle.
Find: (i) the radius of the circle,
(ii) the area of the shaded region. (Take $\pi$ = 3.14 )
View full solution →Find: (i) the radius of the circle,
(ii) the area of the shaded region. (Take $\pi$ = 3.14 )
The shape of the top of a table in a restaurant is that of a segment of a circle with centre O and angle BOD = 90 BO = OD = 60 cm.
Find (i) the area of the top of the table;
(ii) the perimeter of the table. [Take $\pi$ = 3.14 ]
View full solution →Find (i) the area of the top of the table;
(ii) the perimeter of the table. [Take $\pi$ = 3.14 ]
The areas of two concentric circles are $962.5 cm ^2$ and $1386 cm ^2$respectively. Find the width of the ring.
View full solution →Two circles touch externally. The sum of their areas is $117 \pi$ $cm ^2$ and the distance between their centres is 15 cm . Find the radii of the two circles.
View full solution →
Case Study II : Some mementos are ordered by a school for awarding their students on the occasion of Annual Day. Each memento is designed as shown in the figure, where its base ABCD is silver plated from the front side at the rate of ₹50 per $m ^2$. Based on the above information answer the following questions:
1. Area of $\Delta$AOB is :
(a) 50 $cm ^2$ (b) 52 $cm ^2$ (c) 56 $cm ^2$ (d) 60 $cm ^2$
2. Length of the arc CD is :
(a) 44 cm (b) 22 cm (c) 15 cm (d) 11 cm
3. Area of quadrant OCDO is :
(a) 154 $cm ^2$ (b) 77 $cm ^2$ (c) 38.5 $cm ^2$ (d) 30.5 $cm ^2$
4. Area of major sector formed in the figure is :
(a) 154 $cm ^2$ (b) 77 $cm ^2$ (c) 100.5 $cm ^2$ (d) 115.5 $cm ^2$
5. Total cost of silver plating is :
(a) ₹ 575 (b) ₹ 500 (c) ₹ 450 (d) ₹ 400
Area of a sector of central angle 200 of a circle is $770 cm^2$. The length of the corresponding arc of this sector is :
- A$70 \frac{1}{2} cm$
- B$73 \frac{1}{3} cm$
- C76 cm
- ✓$80 \frac{1}{2} cm$
Answer: D.
View full solution →If sum of the areas of two circles with radii r1 and r2 is equal to the area of a circle of radius r, then :
- A$r=r_1+r_2$
- B$r>r_1+r_2$
- C$r^2
- ✓$r^2=r_1^2+r_2^2$
Answer: D.
View full solution →In the figure, if the radius of each circle is 5 cm, then area of the shaded region is :
- A$(400-50 \pi) cm ^2$
- B$(400+100 \pi) cm ^2$
- ✓$(400-100 \pi) cm ^2$
- D$231 cm^2$
Answer: C.
View full solution →Four circular cardboard pieces, each of radius 7 cm are placed in such a way that each piece touches two other pieces. The area of the space enclosed by the four pieces is :
- ✓$42 cm ^2$
- B$40 cm ^2$
- C$21 cm ^2$
- D$18 cm ^2$
Answer: A.
View full solution →The number of rounds that a wheel of diameter $\frac{7}{11} m$ will make in going 4 km is :
- A1600
- B1800
- C1900
- ✓2000
Answer: D.
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